What is the role of entanglements on mechanical properties？? 

The role of entanglements in influencing the mechanical properties of materials is multifaceted and significant across various types of materials, from elastomers to glassy polymers and optomechanical systems. Entanglements, which are essentially physical interactions between polymer chains or fibers, contribute to the mechanical strength, toughness, and self-recovery of elastomers by acting alongside other weak interactions such as ionic bonds. This combination is particularly effective in enhancing the toughness and enabling plastic deformation, which is crucial for materials designed to withstand high stress and strain . In optomechanical systems, entanglements between mechanical oscillators facilitate stable macroscopic quantum entanglement, which is vital for applications in quantum information processing and quantum network construction, showcasing the role of entanglements beyond traditional material science into the realm of quantum mechanics . The resistance to fracture and the ability to undergo viscoplastic flow in polymers subjected to ultrahigh strain rates are also significantly influenced by the presence of entanglements. These entanglements help dissipate kinetic energy during impact, highlighting their importance in dynamic mechanical processes . In athermal fiber networks, entanglements reduce the auxetic effect and maintain inter-fiber contact density under tensile loading, leading to network stiffening and highlighting their role in the mechanical behavior of non-crosslinked fiber networks . Furthermore, the local topology of molecular entanglements at the nanoscale can significantly affect the macroscopic mechanical properties of polymers, such as slowing down the growth and aggregation of nanosized pores during uniaxial stretching . Entanglements also play a critical role in the deformation, fracture, fatigue, and friction of gels and elastomers, although their effects are less understood in these aspects . In glassy polymer thin films, the mechanical properties change with film thickness due to variations in interchain entanglements and molecular mobility, affecting the failure behavior of these materials . The concept of entanglements extends into the geometric connection of mechanical concepts in optical coherence, indicating their influence in optical properties as well . In the quantum realm, entanglement is a sufficient condition for the quantum synchronization of mechanical oscillators, further underscoring its importance in quantum mechanics and potentially in the development of quantum technologies . Although not directly related to mechanical properties, the study of organic solar cells hints at the importance of understanding molecular interactions, including entanglements, for improving mechanical and thermodynamic stability in materials science . In summary, entanglements play a crucial role in enhancing the mechanical properties of materials, including strength, toughness, and stability, across a broad spectrum of applications from traditional material science to quantum technology.

The Role of Intermolecular Entanglements in the Formation of Nanosized Pores during Deformation of Polyethylene: Atomistic Modeling

Entanglements in polyethylene slow down pore growth and aggregation during deformation, impacting mechanical properties by influencing nanoscale dynamics, as shown in the atomistic modeling study.

Tensile behavior of non-crosslinked networks of athermal fibers in the presence of entanglements and friction

Entanglements in non-crosslinked fiber networks confine fibers during tension, stabilize the network via tensegrity, reduce auxetic effects, maintain contact density, and lead to network stiffening.

Influence of Entanglements on Ultrahigh Strain Rate Deformation of Polystyrene Microprojectiles

Entanglements in polystyrene microprojectiles influence ultrahigh strain rate deformation by enabling viscoplastic flow, resisting fracture, and promoting shear banding and crazing, impacting mechanical properties significantly.

Entanglement Between Two Mechanical Oscillators in a Dual-Coupling Optomechanical System

Entanglement enhances quantum correlations between mechanical oscillators, enabling long-lasting and reusable macroscopic quantum entanglement crucial for quantum information processing and network construction.

A constitutive model for elastomers tailored by ionic bonds and entanglements

Entanglements in elastomers enhance stiffness, toughness, and self-recovery by governing the mechanical response through chain stretching and evolution, as per the model developed in the study.